Mites have a habit of doing that. And they are basically born pregnant. I myself would not use neem oil for mites, or use neem oil on a palm. Mites will be on the plant in 3 stages all at once. Eggs, nymphs and adults. Neem and most topical insecticide do not kill the eggs. So you have to keep reapplying every 5-7 days. I prefer a systemic that gives a fast knockdown and of all the adults and nymphs and helps address hatchlings. You still have to do serial application but it works better.
Neem can also cause a buildup over time that interferes with transpiration
